numpy.polynomial.polynomial.polyval — NumPy v1.12 Manual (original) (raw)

numpy.polynomial.polynomial.polyval(x, c, tensor=True)[source]¶

Evaluate a polynomial at points x.

If c is of length n + 1, this function returns the value

$p(x) = c_0 + c_1 * x + ... + c_n * x^n$

The parameter x is converted to an array only if it is a tuple or a list, otherwise it is treated as a scalar. In either case, either _x_or its elements must support multiplication and addition both with themselves and with the elements of c.

If c is a 1-D array, then p(x) will have the same shape as x. If_c_ is multidimensional, then the shape of the result depends on the value of tensor. If tensor is true the shape will be c.shape[1:] + x.shape. If tensor is false the shape will be c.shape[1:]. Note that scalars have shape (,).

Trailing zeros in the coefficients will be used in the evaluation, so they should be avoided if efficiency is a concern.

Parameters:	x : array_like, compatible object If x is a list or tuple, it is converted to an ndarray, otherwise it is left unchanged and treated as a scalar. In either case, x_or its elements must support addition and multiplication with with themselves and with the elements of c. c : array_like Array of coefficients ordered so that the coefficients for terms of degree n are contained in c[n]. If c is multidimensional the remaining indices enumerate multiple polynomials. In the two dimensional case the coefficients may be thought of as stored in the columns of c. tensor : boolean, optional If True, the shape of the coefficient array is extended with ones on the right, one for each dimension of x. Scalars have dimension 0 for this action. The result is that every column of coefficients in_c is evaluated for every element of x. If False, x is broadcast over the columns of c for the evaluation. This keyword is useful when c is multidimensional. The default value is True. New in version 1.7.0.
Returns:	values : ndarray, compatible object The shape of the returned array is described above.

Parameters:

x : array_like, compatible object If x is a list or tuple, it is converted to an ndarray, otherwise it is left unchanged and treated as a scalar. In either case, x_or its elements must support addition and multiplication with with themselves and with the elements of c. c : array_like Array of coefficients ordered so that the coefficients for terms of degree n are contained in c[n]. If c is multidimensional the remaining indices enumerate multiple polynomials. In the two dimensional case the coefficients may be thought of as stored in the columns of c. tensor : boolean, optional If True, the shape of the coefficient array is extended with ones on the right, one for each dimension of x. Scalars have dimension 0 for this action. The result is that every column of coefficients in_c is evaluated for every element of x. If False, x is broadcast over the columns of c for the evaluation. This keyword is useful when c is multidimensional. The default value is True. New in version 1.7.0.

Returns:

values : ndarray, compatible object The shape of the returned array is described above.

Notes

The evaluation uses Horner’s method.

Examples

from numpy.polynomial.polynomial import polyval polyval(1, [1,2,3]) 6.0 a = np.arange(4).reshape(2,2) a array([[0, 1], [2, 3]]) polyval(a, [1,2,3]) array([[ 1., 6.], [ 17., 34.]]) coef = np.arange(4).reshape(2,2) # multidimensional coefficients coef array([[0, 1], [2, 3]]) polyval([1,2], coef, tensor=True) array([[ 2., 4.], [ 4., 7.]]) polyval([1,2], coef, tensor=False) array([ 2., 7.])